Numerical computation of average pillar stress and implications for pillar design

Abstract:

A number of issues relating to the computational aspects of pillar
design are addressed in this paper. The computation of average
pillar stress values is important when attempting to establish
criteria for pillar design and in the analysis of the stability of
tabular pillar layouts. One of the default ‘classic’ numerical methods
that are used to determine pillar stresses is the displacement discontinuity
method. In many instances it is not clearly understood that
this approach does suffer from some limitations, particularly in
relation to the fact that in coarse element simulations, the simulated
average pillar stress (APS) can depend on the chosen mesh size. The
nature of this error is highlighted in this paper and some strategies
are suggested to bound the magnitude of these errors. It is
demonstrated as well that the popular linear stiffness approximation
to pillar or seam compressibility does appear to allow
reasonably accurate estimates of the average pillar stress when
either the pillar height is varied or when the seam modulus differs
from the host rock modulus. A practical implication of this study is
that if the seam modulus is noticeably lower than that of the host
rock, such as for coal seams, it is important to use a linear stiffness
constitutive model for the pillars rather than a ‘rigid’ pillar
assumption. This added complexity seems unnecessary, however,
when simulating hard rock pillars in mines where the seam modulus
is very similar to that of the surrounding rock.